Black hole in a heat bath

Abstract

It was recently pointed out by Barrau et al. that the mass of the Schwarzschild black hole immersed in a heat bath tends to infinity in a finite time. We show that this singularity problem in the black hole mass may be avoided, if the stretched horizon of the black hole is constructed out of a fixed, finite number of discrete constituents, and an appropriate counting is applied to the energy eigenstates of the hole.